Growing exponentials as a probing signal for system identification

In this investigation a variant of the system identification problem has been solved using growing exponentials as the input signal to the system. The system contained two parameters whose values could be varied above and below nominal values. A probing signal basis composed of growing exponentials was matched to the space of patterns defined by small variations in the parameters of the system. The optimum probing signal within the signal space was then selected so as to minimize the covariance matrix of the errors in the measurement of these parameters as the optimizing criterion. Experimental results show that by properly filtering and measuring the response of the system to this optimized probing signal, we may detect and independently measure the simultaneous deviations in the system parameters.